Estimation under model uncertainty

Model selection has had a virtual monopoly on dealing with model uncertainty ever since models were identified as important conduits for statistical inference. Model averaging alleviates some of its deficiencies, but does not offer a practical solution in all settings. We propose an alternative based on linear combinations of the candidate models’ estimators. The general proposal is elaborated for ordinary regression and is illustrated with examples. Some estimators based on invalid models contribute to efficient estimation of certain quantities.